Calculate Distance Between Two Coordinates Decimal Degrees

This calculator helps you determine the distance between two geographic coordinates specified in decimal degrees. The calculation uses the Haversine formula, which is particularly well-suited for measuring distances on a sphere, such as the Earth.

How to Use This Calculator

To calculate the distance between two coordinates:

Enter the latitude and longitude of the first location in decimal degrees.
Enter the latitude and longitude of the second location in decimal degrees.
Select the unit of measurement (kilometers or miles).
Click the "Calculate" button to get the result.

The calculator will display the distance between the two points in the selected unit, along with a visual representation of the coordinates on a map.

The Haversine Formula

The Haversine formula calculates the great-circle distance between two points on a sphere given their longitudes and latitudes. The formula is:

Haversine Formula

a = sin²(Δφ/2) + cos φ₁ ⋅ cos φ₂ ⋅ sin²(Δλ/2)

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Where:

φ is latitude, λ is longitude
R is Earth's radius (mean radius = 6,371km)
Δφ and Δλ are differences in coordinates

The formula accounts for the curvature of the Earth, providing more accurate distance measurements than simpler planar approximations.

Worked Example

Let's calculate the distance between New York City (40.7128° N, 74.0060° W) and Los Angeles (34.0522° N, 118.2437° W) in kilometers.

Example Calculation

Using the Haversine formula:

Δφ = 34.0522° - 40.7128° = -6.6606°

Δλ = 118.2437° - (-74.0060°) = 192.2497°

a = sin²(-6.6606°/2) + cos(40.7128°) ⋅ cos(34.0522°) ⋅ sin²(192.2497°/2)

c = 2 ⋅ atan2(√a, √(1−a))

d = 6,371km ⋅ c ≈ 3,935km

The distance between New York City and Los Angeles is approximately 3,935 kilometers.

FAQ

What is the difference between decimal degrees and degrees-minutes-seconds?: Decimal degrees represent coordinates as single decimal numbers (e.g., 40.7128°), while degrees-minutes-seconds use separate values for degrees, minutes, and seconds (e.g., 40°42'46"N). This calculator uses decimal degrees for simplicity and precision.
Why does the Earth's radius affect the calculation?: The Earth is not a perfect sphere, but using the mean radius (6,371km) provides a good approximation for most purposes. For more precise measurements, you might need to consider the Earth's ellipsoidal shape.
Can I use this calculator for air travel distances?: Yes, this calculator provides a good approximation for air travel distances between two points. However, actual flight paths may vary due to air traffic control, weather conditions, and other factors.
What if I enter coordinates in the wrong order?: The calculator will still produce a result, but it may not be meaningful. Ensure you enter the latitude first, then the longitude for each coordinate.